TSTP Solution File: LCL202-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL202-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:35:23 EDT 2022
% Result : Unsatisfiable 2.28s 2.50s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of clauses : 53 ( 35 unt; 0 nHn; 53 RR)
% Number of literals : 74 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(implies__dfg(not__dfg(or__dfg(p,q)),or__dfg(p,not__dfg(q)))),
file('LCL202-3.p',unknown),
[] ).
cnf(2,axiom,
axiom(implies__dfg(or__dfg(u,u),u)),
file('LCL202-3.p',unknown),
[] ).
cnf(3,axiom,
axiom(implies__dfg(u,or__dfg(v,u))),
file('LCL202-3.p',unknown),
[] ).
cnf(4,axiom,
axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
file('LCL202-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
file('LCL202-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
file('LCL202-3.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
file('LCL202-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL202-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
file('LCL202-3.p',unknown),
[] ).
cnf(15,plain,
axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(16,plain,
axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(19,plain,
( ~ axiom(implies__dfg(u,v))
| ~ theorem(u)
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.1')] ).
cnf(20,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[19,16]),
[iquote('0:SoR:19.0,16.0')] ).
cnf(23,plain,
( ~ theorem(or__dfg(u,not__dfg(v)))
| theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[19,15]),
[iquote('0:SoR:19.0,15.0')] ).
cnf(25,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,4]),
[iquote('0:SoR:19.0,4.0')] ).
cnf(26,plain,
( ~ theorem(u)
| theorem(or__dfg(v,u)) ),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(27,plain,
( ~ theorem(or__dfg(u,u))
| theorem(u) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(35,plain,
( ~ theorem(or__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,or__dfg(u,w))) ),
inference(sor,[status(thm)],[19,5]),
[iquote('0:SoR:19.0,5.0')] ).
cnf(36,plain,
axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(40,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,36]),
[iquote('0:Rew:7.0,36.0')] ).
cnf(48,plain,
( ~ theorem(implies__dfg(u,v))
| theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
inference(sor,[status(thm)],[19,6]),
[iquote('0:SoR:19.0,6.0')] ).
cnf(62,plain,
( ~ axiom(implies__dfg(u,v))
| theorem(or__dfg(v,not__dfg(u))) ),
inference(sor,[status(thm)],[20,8]),
[iquote('0:SoR:20.0,8.1')] ).
cnf(63,plain,
( ~ theorem(implies__dfg(u,or__dfg(v,w)))
| theorem(or__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,40]),
[iquote('0:SoR:19.0,40.0')] ).
cnf(64,plain,
axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
inference(spr,[status(thm),theory(equality)],[7,40]),
[iquote('0:SpR:7.0,40.0')] ).
cnf(66,plain,
axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
inference(rew,[status(thm),theory(equality)],[7,64]),
[iquote('0:Rew:7.0,64.0')] ).
cnf(79,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
inference(sor,[status(thm)],[62,4]),
[iquote('0:SoR:62.0,4.0')] ).
cnf(80,plain,
theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
inference(sor,[status(thm)],[62,3]),
[iquote('0:SoR:62.0,3.0')] ).
cnf(94,plain,
theorem(implies__dfg(u,or__dfg(v,u))),
inference(sor,[status(thm)],[23,80]),
[iquote('0:SoR:23.0,80.0')] ).
cnf(120,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
inference(sor,[status(thm)],[23,79]),
[iquote('0:SoR:23.0,79.0')] ).
cnf(126,plain,
( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
| theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[19,66]),
[iquote('0:SoR:19.0,66.0')] ).
cnf(138,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,or__dfg(w,v))) ),
inference(sor,[status(thm)],[35,26]),
[iquote('0:SoR:35.0,26.1')] ).
cnf(186,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[63,120]),
[iquote('0:SoR:63.0,120.0')] ).
cnf(189,plain,
theorem(or__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[63,94]),
[iquote('0:SoR:63.0,94.0')] ).
cnf(191,plain,
theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[27,189]),
[iquote('0:SoR:27.0,189.0')] ).
cnf(195,plain,
theorem(or__dfg(u,not__dfg(u))),
inference(sor,[status(thm)],[20,191]),
[iquote('0:SoR:20.0,191.0')] ).
cnf(196,plain,
theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
inference(sor,[status(thm)],[63,191]),
[iquote('0:SoR:63.0,191.0')] ).
cnf(200,plain,
theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[7,195]),
[iquote('0:SpR:7.0,195.0')] ).
cnf(202,plain,
theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
inference(sor,[status(thm)],[48,200]),
[iquote('0:SoR:48.0,200.0')] ).
cnf(258,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
inference(sor,[status(thm)],[25,186]),
[iquote('0:SoR:25.0,186.0')] ).
cnf(264,plain,
theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[7,196]),
[iquote('0:SpR:7.0,196.0')] ).
cnf(266,plain,
theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[7,264]),
[iquote('0:Rew:7.0,264.0')] ).
cnf(280,plain,
theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
inference(sor,[status(thm)],[138,195]),
[iquote('0:SoR:138.0,195.0')] ).
cnf(295,plain,
theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),
inference(sor,[status(thm)],[25,280]),
[iquote('0:SoR:25.0,280.0')] ).
cnf(300,plain,
theorem(or__dfg(or__dfg(u,not__dfg(v)),or__dfg(w,v))),
inference(sor,[status(thm)],[138,295]),
[iquote('0:SoR:138.0,295.0')] ).
cnf(434,plain,
( ~ theorem(u)
| theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(res,[status(thm),theory(equality)],[266,9]),
[iquote('0:Res:266.0,9.1')] ).
cnf(839,plain,
( ~ theorem(u)
| ~ theorem(implies__dfg(u,v))
| theorem(v) ),
inference(res,[status(thm),theory(equality)],[434,9]),
[iquote('0:Res:434.1,9.1')] ).
cnf(1387,plain,
( ~ theorem(or__dfg(u,v))
| theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
inference(res,[status(thm),theory(equality)],[202,9]),
[iquote('0:Res:202.0,9.1')] ).
cnf(3769,plain,
theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
inference(sor,[status(thm)],[1387,258]),
[iquote('0:SoR:1387.0,258.0')] ).
cnf(4780,plain,
theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
inference(sor,[status(thm)],[23,3769]),
[iquote('0:SoR:23.0,3769.0')] ).
cnf(4801,plain,
theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
inference(sor,[status(thm)],[126,4780]),
[iquote('0:SoR:126.0,4780.0')] ).
cnf(4804,plain,
( ~ theorem(or__dfg(u,v))
| theorem(implies__dfg(not__dfg(v),u)) ),
inference(sor,[status(thm)],[839,4801]),
[iquote('0:SoR:839.1,4801.0')] ).
cnf(6185,plain,
theorem(implies__dfg(not__dfg(or__dfg(u,v)),or__dfg(w,not__dfg(v)))),
inference(sor,[status(thm)],[4804,300]),
[iquote('0:SoR:4804.0,300.0')] ).
cnf(6397,plain,
$false,
inference(unc,[status(thm)],[6185,1]),
[iquote('0:UnC:6185.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL202-3 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 02:13:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.28/2.50
% 2.28/2.50 SPASS V 3.9
% 2.28/2.50 SPASS beiseite: Proof found.
% 2.28/2.50 % SZS status Theorem
% 2.28/2.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.28/2.50 SPASS derived 6057 clauses, backtracked 0 clauses, performed 0 splits and kept 2814 clauses.
% 2.28/2.50 SPASS allocated 83839 KBytes.
% 2.28/2.50 SPASS spent 0:00:02.12 on the problem.
% 2.28/2.50 0:00:00.04 for the input.
% 2.28/2.50 0:00:00.00 for the FLOTTER CNF translation.
% 2.28/2.50 0:00:00.24 for inferences.
% 2.28/2.50 0:00:00.00 for the backtracking.
% 2.28/2.50 0:00:01.77 for the reduction.
% 2.28/2.50
% 2.28/2.50
% 2.28/2.50 Here is a proof with depth 16, length 53 :
% 2.28/2.50 % SZS output start Refutation
% See solution above
% 2.28/2.50 Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 2.28/2.50
%------------------------------------------------------------------------------